Barack Obama used his long-heralded speech to the Muslim world today to call for a new beginning in relations and made an impassioned plea for a two-state solution to resolve the bitter conflict between Israel and the Palestinians.

Seeking to draw a line under the war in Iraq, Guantánamo Bay and other Bush policies, Obama went out of his way to display understanding of the causes of Muslim resentment and mistrust of the west.

But as he left for Germany and France for D-Day celebrations his landmark address drew mixed reviews for a performance many found sensitively crafted and sincere but lacking substance or novelty.

"I have come here to seek a new beginning between the US and Muslims around the world, one based upon mutual interest and mutual respect," the president told an invited audience at Cairo University. "America and Islam are not exclusive, and need not be in competition."

Obama's messages on the hot-button issues of Israel, the Palestinians and Iran did not break new ground, while passages on Afghanistan, Iraq and fighting violent extremism also replayed familiar themes. Still, some of his strongest words were reserved for the ever-contentious issue of Israel and the Palestinians, whose life under occupation was "intolerable".

There was loud applause when he said emphatically: "The US does not accept the legitimacy of continued Israeli settlements. This construction violates previous agreements and undermines efforts to achieve peace. It is time for these settlements to stop."

But comments that presage a clash with Binyamin Netanyahu's rightwing government were balanced with an appeal to the Palestinian movement Hamas to abandon violence. "It is a sign of neither courage nor power to shoot rockets at sleeping children, or to blow up old women on a bus," he said.

Obama also referred to America's "unbreakable bond" with Israel, which he coupled with a bold attack on "baseless, ignorant and hateful" denial of the Nazi Holocaust – a staple of the hardline Iranian president, Mahmoud Ahmadinejad.

The Cairo speech had been billed as one of Obama's most important, and was keenly awaited after a fleeting visit to Iraq, a Persian new year message to Iran, and a speech to the Turkish parliament in Ankara.

As expected, he referred to his own Muslim roots, mentioning the azaan call to prayer that he heard while a child in Indonesia. He played the religious card deftly. America would never be at war with Islam. "The Holy Qur'an teaches that whoever kills an innocent, it is as if he has killed all mankind; and whoever saves a person, it is as if he has saved all mankind.

"The faith of over a billion people is so much bigger than the narrow hatred of a few. Islam is not part of the problem in combating violent extremism – it is an important part of promoting peace."

He referred to his decision to close the Guantánamo Bay detention camp and did not use the Bush-era phrase "war on terror". Religious freedom and women's rights were also emphasised – a challenge to intolerance and bigotry.

Obama's comments on democracy – a burning issue in US allies Egypt and Saudi Arabia and most Arab countries – were detailed but non-specific, a disappointment if not a surprise to activists.

"America does not presume to know what is best for everyone, just as we would not presume to pick the outcome of a peaceful election," the president said. "But I do have an unyielding belief that all people yearn for certain things: the ability to speak your mind and have a say in how you are governed; government that is transparent and doesn't steal from the people; the freedom to live as you choose.

''Those are not just American ideas, they are human rights, and that is why we will support them everywhere."

Reaction was varied. In Damascus, the Hamas leader Khaled Meshal told Time magazine: "Undoubtedly Obama speaks a new language. We are looking for more than just mere words … We are keen to contribute to this. But we [believe that can not happen] merely with words."

"It was basically a very conciliatory speech," said Hisham Kassem, one of Egypt's leading commentators. "Obama was saying 'I'm not George Bush'. But there was very little policy and very little you could hold him accountable to."

Mohamed Habib, deputy leader of Egypt's Muslim Brotherhood, the Islamist movement that poses the strongest opposition to Hosni Mubarak's authoritarian regime, called the speech "a public relations address". Iran and Hezbollah in Lebanon both attacked it.

In the speech Obama defended US strategy in Afghanistan and Iraq but made it clear he did not wish to maintain a permanent military presence in either country.

Obama's message on Iran – where Ahmadinejad is facing crucial presidential elections next week – repeated a commitment to "mutual respect" between the old adversaries.

But he issued a warning on the burning issue of nuclear weapons. "We have reached a decisive point. This is not simply about America's interests. It is about preventing a nuclear arms race in the Middle East that could lead this region and the world down a hugely dangerous path."